I re-read some of Edersheim's great work, the Life and times of Jesus the Messiah and he agrees with you to a point that I am willing to agree with as well.
The gist of it all is, though, that Christ was going away, and He was leaving the work of the church that He had established, to the apostles and to the disciples. Later in Matthew 18, he addresses all of them with the same concerns.
Peter did preach to the centurion and he did have the vision about the animals that opened up the church to the Gentiles.
Still, He gave all of them the keys to the kingdom, and as we know, the kingdom is spiritual and the kingdom is within, and so these have to be spiritual keys. Making disciples and guiding those disciples in a Christian life, and in establishing church procedures were all included in the stewardship. Peter was one pillar, there are 12 others.
Edersheim also says that "loosing" and "binding" refers to things that are prohibited and permitted. In Rabbinic law the terms could refer to pardoning and forgiving but this is not the case with Christ, and forgiveness of sins is not to be considered the meaning
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As the Acts, chapter ten, account points out Cornelius was sent by an angel to find Peter the day before Peter was informed by vision what had already been put into force.
What Peter would loose would be the thing already loosed (or bound) and that is the sense of the Greek. (Matt. 16:19-21)
Since the Greek doesn't have tenses in the way the English does the tense expressed is often misplaced.
The sense of the Greek is of an action begun in the past and is or has effects continuing into the present.
Try googling “dedemenon greek” for some better explanations.
So no, the binding and loosing was not forgiveness of sins.
As to the kingdom being “within”, I assume you mean being a condition within us as individuals, but I think that is a misunderstanding what the kingdom is and what was meant by “within”.
Acts 10:9 About noon the following day as they were on their journey and approaching the city, Peter went up on the roof to pray. 10He became hungry and wanted something to eat, and while the meal was being prepared, he fell into a trance. 11He saw heaven opened and something like a large sheet being let down to earth by its four corners. 12It contained all kinds of four-footed animals, as well as reptiles of the earth and birds of the air. 13Then a voice told him, "Get up, Peter. Kill and eat."
14"Surely not, Lord!" Peter replied. "I have never eaten anything impure or unclean."
15The voice spoke to him a second time, "Do not call anything impure that God has made clean."
16This happened three times, and immediately the sheet was taken back to heaven.
17While Peter was wondering about the meaning of the vision, the men sent by Cornelius found out where Simon's house was and stopped at the gate. 18They called out, asking if Simon who was known as Peter was staying there.
19While Peter was still thinking about the vision, the Spirit said to him, "Simon, three men are looking for you. 20So get up and go downstairs. Do not hesitate to go with them, for I have sent them."
21Peter went down and said to the men, "I'm the one you're looking for. Why have you come?"
22The men replied, "We have come from Cornelius the centurion. He is a righteous and God-fearing man, who is respected by all the Jewish people. A holy angel told him to have you come to his house so that he could hear what you have to say." 23Then Peter invited the men into the house to be his guests.